77edo: Difference between revisions

Wikispaces>xenwolf
**Imported revision 539467156 - Original comment: **
Wikispaces>Gedankenwelt
**Imported revision 539554354 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2015-02-03 05:52:37 UTC</tt>.<br>
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-02-03 14:09:35 UTC</tt>.<br>
: The original revision id was <tt>539467156</tt>.<br>
: The original revision id was <tt>539554354</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=&lt;span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;77 tone Equal Temperament&lt;/span&gt;=  
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=&lt;span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;77 tone Equal Temperament&lt;/span&gt;=  


77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine]], the 31&amp;46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto.
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine|valentine]], the 31&amp;46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto.


77et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]].
77et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]].
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||&gt; 4 ||&gt; 62.338 ||= 28/27, 26/25 ||
||&gt; 4 ||&gt; 62.338 ||= 28/27, 26/25 ||
||&gt; 5 ||&gt; 77.922 ||= 21/20, 25/24 ||
||&gt; 5 ||&gt; 77.922 ||= 21/20, 25/24 ||
||&gt; 6 ||&gt; 93.506 ||=   ||
||&gt; 6 ||&gt; 93.506 ||= 135/128 ||
||&gt; 7 ||&gt; 109.091 ||= 16/15 ||
||&gt; 7 ||&gt; 109.091 ||= 16/15 ||
||&gt; 8 ||&gt; 124.675 ||= 15/14 ||
||&gt; 8 ||&gt; 124.675 ||= 15/14 ||
||&gt; 9 ||&gt; 140.260 ||= 13/12 ||
||&gt; 9 ||&gt; 140.260 ||= 13/12 ||
||&gt; 10 ||&gt; 155.844 ||= 12/11, 11/10 ||
||&gt; 10 ||&gt; 155.844 ||= 12/11, 11/10 ||
||&gt; 11 ||&gt; 171.429 ||=   ||
||&gt; 11 ||&gt; 171.429 ||= 72/65 ||
||&gt; 12 ||&gt; 187.013 ||= 10/9 ||
||&gt; 12 ||&gt; 187.013 ||= 10/9 ||
||&gt; 13 ||&gt; 202.597 ||= 9/8 ||
||&gt; 13 ||&gt; 202.597 ||= 9/8 ||
||&gt; 14 ||&gt; 218.182 ||=   ||
||&gt; 14 ||&gt; 218.182 ||= 256/225 ||
||&gt; 15 ||&gt; 233.766 ||= 8/7 ||
||&gt; 15 ||&gt; 233.766 ||= 8/7 ||
||&gt; 16 ||&gt; 249.351 ||= 15/13 ||
||&gt; 16 ||&gt; 249.351 ||= 15/13 ||
Line 37: Line 37:
||&gt; 19 ||&gt; 296.104 ||= 32/27, 13/11 ||
||&gt; 19 ||&gt; 296.104 ||= 32/27, 13/11 ||
||&gt; 20 ||&gt; 311.688 ||= 6/5 ||
||&gt; 20 ||&gt; 311.688 ||= 6/5 ||
||&gt; 21 ||&gt; 327.273 ||=   ||
||&gt; 21 ||&gt; 327.273 ||= 98/81 ||
||&gt; 22 ||&gt; 342.857 ||= 11/9, 39/32 ||
||&gt; 22 ||&gt; 342.857 ||= 11/9, 39/32 ||
||&gt; 23 ||&gt; 358.442 ||= 16/13 ||
||&gt; 23 ||&gt; 358.442 ||= 16/13 ||
Line 47: Line 47:
||&gt; 29 ||&gt; 451.948 ||= 13/10 ||
||&gt; 29 ||&gt; 451.948 ||= 13/10 ||
||&gt; 30 ||&gt; 467.532 ||= 21/16 ||
||&gt; 30 ||&gt; 467.532 ||= 21/16 ||
||&gt; 31 ||&gt; 483.117 ||=   ||
||&gt; 31 ||&gt; 483.117 ||= 120/91 ||
||&gt; 32 ||&gt; 498.701 ||= 4/3 ||
||&gt; 32 ||&gt; 498.701 ||= 4/3 ||
||&gt; 33 ||&gt; 514.286 ||= 27/20 ||
||&gt; 33 ||&gt; 514.286 ||= 27/20 ||
Line 62: Line 62:
||&gt; 44 ||&gt; 685.714 ||= 40/27 ||
||&gt; 44 ||&gt; 685.714 ||= 40/27 ||
||&gt; 45 ||&gt; 701.299 ||= 3/2 ||
||&gt; 45 ||&gt; 701.299 ||= 3/2 ||
||&gt; 46 ||&gt; 716.883 ||=   ||
||&gt; 46 ||&gt; 716.883 ||= 91/60 ||
||&gt; 47 ||&gt; 732.468 ||= 32/21 ||
||&gt; 47 ||&gt; 732.468 ||= 32/21 ||
||&gt; 48 ||&gt; 748.052 ||= 20/13 ||
||&gt; 48 ||&gt; 748.052 ||= 20/13 ||
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||&gt; 54 ||&gt; 841.558 ||= 13/8 ||
||&gt; 54 ||&gt; 841.558 ||= 13/8 ||
||&gt; 55 ||&gt; 857.143 ||= 18/11, 64/39 ||
||&gt; 55 ||&gt; 857.143 ||= 18/11, 64/39 ||
||&gt; 56 ||&gt; 872.727 ||=   ||
||&gt; 56 ||&gt; 872.727 ||= 81/49 ||
||&gt; 57 ||&gt; 888.312 ||= 5/3 ||
||&gt; 57 ||&gt; 888.312 ||= 5/3 ||
||&gt; 58 ||&gt; 903.896 ||= 27/16, 22/13 ||
||&gt; 58 ||&gt; 903.896 ||= 27/16, 22/13 ||
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||&gt; 61 ||&gt; 950.649 ||= 26/15 ||
||&gt; 61 ||&gt; 950.649 ||= 26/15 ||
||&gt; 62 ||&gt; 966.234 ||= 7/4 ||
||&gt; 62 ||&gt; 966.234 ||= 7/4 ||
||&gt; 63 ||&gt; 981.818 ||=   ||
||&gt; 63 ||&gt; 981.818 ||= 225/128 ||
||&gt; 64 ||&gt; 997.403 ||= 16/9 ||
||&gt; 64 ||&gt; 997.403 ||= 16/9 ||
||&gt; 65 ||&gt; 1012.987 ||= 9/5 ||
||&gt; 65 ||&gt; 1012.987 ||= 9/5 ||
||&gt; 66 ||&gt; 1028.571 ||=   ||
||&gt; 66 ||&gt; 1028.571 ||= 65/36 ||
||&gt; 67 ||&gt; 1044.156 ||= 11/6, 20/11 ||
||&gt; 67 ||&gt; 1044.156 ||= 11/6, 20/11 ||
||&gt; 68 ||&gt; 1059.740 ||= 24/13 ||
||&gt; 68 ||&gt; 1059.740 ||= 24/13 ||
||&gt; 69 ||&gt; 1075.325 ||= 28/15 ||
||&gt; 69 ||&gt; 1075.325 ||= 28/15 ||
||&gt; 70 ||&gt; 1090.909 ||= 15/8 ||
||&gt; 70 ||&gt; 1090.909 ||= 15/8 ||
||&gt; 71 ||&gt; 1106.494 ||=   ||
||&gt; 71 ||&gt; 1106.494 ||= 256/135 ||
||&gt; 72 ||&gt; 1122.078 ||= 40/21, 48/25 ||
||&gt; 72 ||&gt; 1122.078 ||= 40/21, 48/25 ||
||&gt; 73 ||&gt; 1137.662 ||= 27/14, 25/13 ||
||&gt; 73 ||&gt; 1137.662 ||= 27/14, 25/13 ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;77edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x77 tone Equal Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;77 tone Equal Temperament&lt;/span&gt;&lt;/h1&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;77edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x77 tone Equal Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;77 tone Equal Temperament&lt;/span&gt;&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and &lt;a class="wiki_link" href="/7_4"&gt;7/4s&lt;/a&gt; less flat than that, it represents an excellent tuning choice for both &lt;a class="wiki_link" href="/Valentine"&gt;Valentine&lt;/a&gt;, the 31&amp;amp;46 temperament, and &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;starling&lt;/a&gt;, the 126/125 &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as &lt;a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit"&gt;11-limit starling&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20family#Oxpecker"&gt;oxpecker&lt;/a&gt; temperaments. It also gives the optimal patent val for various members of the &lt;a class="wiki_link" href="/unicorn%20family"&gt;unicorn family&lt;/a&gt;, with a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; of 4\77 instead of the 5\77 which gives valentine. These are 7-limit &lt;a class="wiki_link" href="/Unicorn%20family#Alicorn"&gt;alicorn&lt;/a&gt; and 11- and 13-limit camahueto.&lt;br /&gt;
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and &lt;a class="wiki_link" href="/7_4"&gt;7/4s&lt;/a&gt; less flat than that, it represents an excellent tuning choice for both &lt;a class="wiki_link" href="/Valentine"&gt;valentine&lt;/a&gt;, the 31&amp;amp;46 temperament, and &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;starling&lt;/a&gt;, the 126/125 &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as &lt;a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit"&gt;11-limit starling&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20family#Oxpecker"&gt;oxpecker&lt;/a&gt; temperaments. It also gives the optimal patent val for various members of the &lt;a class="wiki_link" href="/unicorn%20family"&gt;unicorn family&lt;/a&gt;, with a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; of 4\77 instead of the 5\77 which gives valentine. These are 7-limit &lt;a class="wiki_link" href="/Unicorn%20family#Alicorn"&gt;alicorn&lt;/a&gt; and 11- and 13-limit camahueto.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
77et tempers out 32805/32768 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, 126/125, 1029/1024 and 6144/6125 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, 121/120, 176/175, 385/384 and 441/440 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;.&lt;br /&gt;
77et tempers out 32805/32768 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, 126/125, 1029/1024 and 6144/6125 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, 121/120, 176/175, 385/384 and 441/440 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;.&lt;br /&gt;
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         &lt;td style="text-align: right;"&gt;93.506&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;93.506&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;135/128&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td style="text-align: right;"&gt;171.429&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;171.429&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;72/65&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 280: Line 280:
         &lt;td style="text-align: right;"&gt;218.182&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;218.182&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;256/225&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td style="text-align: right;"&gt;327.273&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;327.273&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;98/81&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 416: Line 416:
         &lt;td style="text-align: right;"&gt;483.117&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;483.117&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;120/91&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 536: Line 536:
         &lt;td style="text-align: right;"&gt;716.883&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;716.883&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;91/60&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 616: Line 616:
         &lt;td style="text-align: right;"&gt;872.727&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;872.727&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;81/49&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 672: Line 672:
         &lt;td style="text-align: right;"&gt;981.818&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;981.818&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;225/128&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 696: Line 696:
         &lt;td style="text-align: right;"&gt;1028.571&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1028.571&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;65/36&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 736: Line 736:
         &lt;td style="text-align: right;"&gt;1106.494&lt;br /&gt;
         &lt;td style="text-align: right;"&gt;1106.494&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;256/135&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;